A time for cuddles, smiles and no doubt tears – and not just from the newborn. A time for rest, a warm glow, and also for new discoveries. “Look at those little fingers!” “He’s got your nose…” “Gosh, he’s heavy!” And of course, “How does this work?”.

The first nappy was changed, we are told, by the father, William Wales, a 31-year-old helicopter search and rescue pilot. Let’s leave royal titles aside for the moment, because in those four hours after the birth of their first child, they were just William and Kate, just a new mum and a new dad, caught up in the wonder of it all, the most miraculous thing to happen to anyone in the world, ever, as far as they were concerned. Doesn’t every new parent feel that way? Assuming that all is well.

We don’t know the dramas that went on inside St Mary’s Hospital in Paddington. We may never do so, quite properly. Mercifully, though, there seem to have been no problems. The labour was not too long, the birth was natural and the baby boy arrived on Monday July 22 at 4.24pm.

Outside, half the world was waiting. Hundreds of reporters were gathered in the street, sending live pictures of the hospital to millions of people across the planet. The people of Australia, New Zealand and Canada were watching, of course. There was interest in the birth of a future head of state, from Belize to Tuvalu. But the largest battalion of camera crews was from the United States, a nation that has had no practical stake in royalty since it sacked King George III in 1776.

Here in Britain, even republicans were grumbling with smiles on their faces, putting politics aside to wish the baby well. The sun was shining. It was beating down. The heatwave was stretching on and on, London was looking at its finest since the Olympics, a golden city again.

Sporting success had cheered everybody up, for the second summer running. “Sir” Andy Murray had broken the British curse at Wimbledon. A British rider had just won the Tour de France, again. We’d thrashed the Australians at cricket, again. The players had met the Queen before the Second Test at Lords. She was a happy monarch indeed, pleased and strengthened by the way her people had embraced the Diamond Jubilee celebrations – and now with a great-grandchild on the way, to set a royal seal on a sizzling summer.

Social networks were frantic with wonder about when the baby would come, how much it would weigh, whether it would be a boy or a girl, what it would be called. Such speculation radiates from family and friends when a child is about to be born. In this case, it was radiating to the ends of the earth,

So here was a marvellous secret. For four hours and five minutes on Monday afternoon, nobody outside the closest circle knew that the baby had arrived.

The announcement of his arrival was delayed in order to give the parents time to bond with their baby, we are told, and for them to make phone calls to waiting great-grandparents, grandparents, aunts and uncles.

No nurse or surgeon tweeted. No police officer dropped a heavy hint. No reporter outside had any clue what was happening inside the Lindo Wing.

For that secret, sacred time, it was all so simple. A young mother, a young father, and a very young son gurgling up at them both.

It could not last, of course. Layers of portent and meaning were already wrapping themselves around the child like swaddling clothes.

His parents knew all too well that this was to be a public life. The Duchess of Cambridge has been followed by the cameras since she was an undergraduate called Kate Middleton who dared to fall in love with a prince. The Duke has experienced it since the beginning of his life, when he was born in the same hospital as his son, in similar circumstances, in 1982. His own mother, Diana, Princess of Wales, once hailed as one of the most famous and beautiful women in the world, lost her life in a car accident as she tried to escape the attentions of the paparazzi. So both parents knew what lay in store for their son, out there beyond the security doors.

His Royal Highness Prince Baby of Cambridge did not have a name yet, but he had a title. He was third in line to the throne, after his father and grandfather. If all went well, he could expect to become the 43rd monarch since William the Conqueror.

This fragile little thing would one day be the head of the Armed Forces, the Supreme Governor of the Church of England, and head of state in 16 countries around the world (unless a few had turned republican in the meantime).

Would they call him George, as the bookmakers fancied? James? Alexander? John? Paul? Ringo? Maybe not. He was likely to become head of the Commonwealth of 54 nations, with two billion citizens. No wonder his parents took a little time out to reflect and to get to know him, before taking their son out to say hello to the world.

Was the baby late? There was a great deal of confusion about the due date. Some people said it was July 13, some July 19. Others noted that his future grandmother, Carole Middleton, had said the child would be born a Leo.

She was just half an hour out. The star sign’s month was due to begin at 5pm. If Mrs Middleton knew more than most about it, that was no surprise. She was about to become the most important woman in the young prince’s life, after his mother.

The Duke and Duchess of Cambridge have not hired a full-time nanny, largely because, at the age of just 58, the new Granny has the energy and will to give her daughter all the hands-on help she needs.

The couple had been staying at the Middleton family home in Bucklebury, Berkshire, but they slipped back into London on the Friday night before the birth. Their two-bedroom cottage in the grounds of Kensington Palace is only a few minutes drive from St Mary’s Hospital, particularly if you happen to have a police escort.

The weekend passed. Nothing happened. Then, in the early hours of Monday morning, with a full moon and thunder in the air, the Duchess went into labour.

“We took a guess. It was a full moon so we thought, why not come down?” said Jesal Parshotam, a freelance photographer who was standing outside St Mary’s Hospital at 5.30am on Monday when a dark blue Ford Galaxy people carrier with blacked-out windows arrived at a side entrance, followed by a blue Saab 95. By the time he realised who was in the first car, they had already gone inside the hospital.

“It was a very swift manoeuvre,” he said. “The Duchess went in and the cars were gone very quickly – within a minute. That was it.”

He declared what he had seen on Twitter, but few people believed him. There had been so many false alarms. However, at 7.30am it was announced that the Duchess of Cambridge had indeed been admitted. The Telegraph’s chief reporter, Gordon Rayner, learnt that she was in the early stages of labour, which “suggests she wasn’t induced”.

The announcement was not made until she was settled into her private room, having been seen by Marcus Setchell, the Queen’s physician. This 69-year-old grandfather had delayed his retirement, and would lead the medical team.

As soon it was known that she was in labour, royal correspondents began to talk to their television cameras in the street outside, sharing the news but having little more to say. They would have to improvise for hours.

Simon McCoy, reporting for the BBC, made the daring decision to tell the truth to camera, with entertaining results: “Plenty more to come from here, none of it news of course, but that won’t stop us ... let’s speculate, because that’s all we can do.”

Patrick O’Brien, a consultant obstetrician, told the Telegraph that the average weight was eight pounds two ounces and the average length of labour for a first time mother was about 12 hours. The baby was likely to be born in the late afternoon or early evening.

“When you reach fully dilated usually you wait for an hour or so to allow the baby’s head to come as low as possible, and then you push – and the pushing is about an hour to an hour and a half.”

Somebody asked for an opinion from Dame Helen Mirren, who had won an Oscar for playing the lead in the film The Queen, She felt for the Duchess: “That’s weird, isn’t it. everyone knowing you’re in labour? That must be so uncomfortable.”

The announcement of the royal birth was meant to be a moment of high drama. It was all set out in advance. The doctors at the hospital would sign a statement on a sheet of foolscap paper – the protocol was specific about the size – and this would be carried to Buckingham Palace, to be placed on a golden easel at the gates.

Nobody would know the details until an authorised camera operator zoomed in on the statement. Only it didn’t happen like that at all. Before the sheet of paper had even left the hospital, a press release was sent out by email at 8.29pm.

“The Duchess of Cambridge was safely delivered of a son at 4.24pm. The baby weighs 8lbs 6oz. The Duke of Cambridge was present for the birth … Her Royal Highness and her child are both doing well and will remain in hospital overnight.”

This was also posted on the Clarence House Twitter feed. More than half a million people tweeted about the boy. The Archbishop of York, Dr John Sentamu, called him “a great gift of God”.

So we already knew what had happened as the television news cameras followed the somewhat forlorn journey of the previously all-important piece of paper, in a Jaguar from the hospital to the palace. It was framed there and carried out to the easel by a footman, Badar Azim, and the Queen’s press secretary Ailsa Anderson, who brought a dignity to the moment that was remarkable, in the circumstances.

On Twitter, Stephen Fry wrote: “The official easel. We really are a marvellously bonkers country.”

On the steps of the hospital, a town crier with long red, white and blue feathers in his tricorne hat rang his bell and announced the news. “Oh yea, oh yea, oh yea!”

The Prince of Wales released a statement by more modern means, saying he and the Duchess of Cornwell were overjoyed. “Grandparenthood is a unique moment in anyone’s life, as countless kind people have told me in recent months, so I am enormously proud and happy to be a grandfather for the first time and we are eagerly looking forward to seeing the baby in the near future.”

Over in Berkshire, at the Old Boot pub where the Middletons – and some of their royal in-laws – go to drink, there were great celebrations. “When we heard the announcement, the place just exploded,” said the owner John Haley, a guest at the royal wedding in 2011. “We are all having a massive party, it’s a great atmosphere and it’s all kicked off. It’s great that Kate and her son are doing well.”

The fountain in Trafalgar Square was illuminated in blue to mark the birth of the boy. So was Marble Arch and the top of City Hall. The same was true of the Niagara Falls in Canada and the Story Bridge in Brisbane.

The Australian Prime Minister Kevin Rudd struck a note of friendly informality that flirted with silliness, when he said: “I think all Australians, at the bottom of their hearts, wish the Royal Bub all the best.”

His British counterpart David Cameron came out of No 10 to say: “It is an important moment in the life of our nation but, I suppose, above all it is a wonderful moment for a warm and loving couple who have got a brand new baby boy.”

He added: “It has been a remarkable few years for our royal family – a royal wedding that captured people’s hearts, that extraordinary and magnificent jubilee and now this royal birth – all from a family that has given this nation so much incredible service.”

The surgeon-gynaecologist Marcus Setchell emerged from the hospital to tell reporters that the new prince was “a wonderful, beautiful baby”.

There was no hint of a name. Nor was there any sign of Prince William, who had decided to break with royal protocol and spend the night on a camp bed in his wife’s suite. He issued a statement which simply read: “We could not be happier.”

The thunder clapped, the heavens opened, the guns began to fire and the bells began to ring. Everybody knows you should tiptoe around the place when a baby has just been born, but there was not a chance of that in London on Tuesday.

The grandparents were racing towards the hospital from different parts of the country, but as they did so the King’s Troop of the Royal Horse Artillery began firing heavy cannons in Green Park. They fired 21 very loud blanks in salute to the child, with 20 more because they were in a royal park. Over at the Tower of London, the guns were fired 62 times.

The bells of Westminster Abbey also began to sound, and the 5,000 changes of the Cambridge Surprise Royal peal took more than three hours. It was a glorious noise.

People were now queuing in the rain for the right to stand in front of the famous easel at Buckingham Palace, although the police were asking them not to linger for more than three seconds each.

As all this was going on, Michael and Carole Middleton won the race to St Mary’s. One or two of the fussier royal watchers muttered that it should have been the Queen who visited first, or at least the Prince of Wales; but he was still on his way down from Yorkshire by helicopter.

The Middletons had only to come from Berkshire. They arrived looking tanned, relaxed and of course delighted. She was wearing a blue summer dress, nipped in at the waist. He was in white slacks, a blue and white candy-striped shirt and a navy blazer, as if he had just come up from Cowes.

They were taken to and from the hospital in pre-booked taxis, one of whose drivers was Traci Mitchell, 49, from the Isle of Dogs. She congratulated them, saying afterwards: “They said thank you very much. Very down to earth people, they seemed. She was kind of bewildered by it all.”

This was the day a member of the House of Lords chose to complain about royal baby fever, saying it was “not a great day for social mobility”. He can’t have been talking about the Middletons, whose social stock has soared beyond all dreams.

The couple met when Carole was a member of British Airways cabin crew and Michael was a flight dispatcher, but she later started a business on their kitchen table, selling party bags to mothers in her village. Party Pieces is now said to be worth £30m and rising. Not a fortune by royal standards, perhaps, but enough to send your children to the best private schools, and to a university attended by a prince.

Besides their daughter, the Middletons have given Prince William something else that is priceless: a happy, stable family life.

Penny Junor, a biographer of Prince William, has said: “I think he has looked at the Middleton model and seen what a happy family they are, how united they are and how they have fun together and he would like to reproduce that.”

They have also become experts at discretion. Leaving the hospital after their brief visit on Tuesday afternoon, Carole Middleton was asked if she had given any advice on the name. She grinned and said: “Absolutely not!”

Her husband was contentedly silent, but Mrs Middleton said that the new mother and her child were “both doing well, we’re so thrilled”.

We were about to find that out for ourselves. The royal hairdresser had been seen arriving at the hospital with a suitcase. Amanda Cook Tucker, 41, styles the Duchess of Cambridge’s remarkably lustrous locks. Her presence could only mean they were about to be seen in public again, very soon.

This was confirmed when the Prince of Wales and the Duchess of Cornwall arrived, dressed far more formally than the Middletons, as is their habit, but both looking absolutely ecstatic. When he emerged from the hospital, Prince Charles was so relaxed he appeared to have been at the laughing gas. Asked how the couple were coping. “You wait and see, you will see in a minute.”

So it was that at 7.15pm on Tuesday evening, the royal couple came out of the hospital at last, to show off their child. She looked happy, if naturally tired, in a cornflower blue dress with white polka dots by Jenny Packham.

The British designer’s website appeared to crash, such was the immediate demand.

The dress echoed the rather more voluminous one worn in the same street by Princess Diana 31 years earlier. The photographs highlighted that Kate was wearing Diana’s diamond and sapphire ring, given to her by William on their engagement in 2010. He said then, of his mother: “Obviously, she’s not going to be around to share in any of the fun and excitement, so this is my way of keeping her sort of close to it all.”

Memories of Diana were certainly conjured up as the couple stood outside the hospital, not least by their informality. William was wearing a blue, open-necked shirt with the sleeves rolled up, nothing like the pinstripe suit his father had worn in the same place and in the same situation in 1982. Were those jeans the Duke was wearing? They looked like it.

The Duchess made no attempt to hide her postpartum bump. Those days were gone. Once again, the body language was a reminder that they are a couple who fell in love, took time to let it grow and are unafraid to let their intimacy show.

William called his wife Poppet, and took the baby with the instinctive hip swivel of a man who had already soothed away its tears.

“He’s got her looks, thankfully,” he said, as his wife protested meekly, “No, no, I’m not sure about that.”

As for the child’s downy hair, he said: “He’s got way more than me. Thank God.”

The baby had “a good pair of lungs on him, that’s for sure” and was “a big boy, he’s quite heavy”. The tiny prince’s surprisingly long fingers poked out from his white shawl, almost in a royal wave.

The £45 shawl had been made by GH Hurt and Sons of Nottinghamshire. Sales rocketed, immediately. A spokeswoman said that night: “We’re working incredibly hard. It’s taken us by surprise because we’re a small family firm of less than 20 employees.”

Handing his son back to the mother, Prince William said he had already changed the first nappy. She said, “He’s very good at it.”

The Prince insisted they were still working on a name, adding awkwardly: “It’s the first time we’ve seen him really, so we’re having a proper chance to catch up.”

Would it be George? All the proud father would say was: “Wait and see.”

The Duke clicked the baby seat containing his son into the back of a Range Rover with ease, and climbed into the front. Britax, the Anglo-German company that makes the seat, which hadn’t known the royal couple owned one, declared itself “delighted”.

The Duchess sat beside the boy as they were driven off for the short journey back to Kensington Palace, which is expected to become their permanent home when Prince William ends his spell of duty as a search and rescue pilot in September.

Princess Margaret’s former home, Apartment 1a, is currently being refurbished to suit them, at the cost of £1m. It is not yet known whether the Duke of Cambridge will remain in the RAF, move within the armed forces or retire to concentrate on full-time royal duties. Either way, the new baby’s early life will not be dominated by the nanny in the nursery, as his was.

Diana was a tactile, hands-on mother who fought the royal system, but she was too young to beat it entirely. Catherine, the Duchess of Cambridge, is 31 years old. She knows what she wants, and who she wants be at her side, and that is her mother.

The Duchess and her son are expected to spend a lot of their free time in Bucklebury, but when they are in London they will find the palace has a large garden in which to play, behind reassuringly high walls.

The young family will also have Anmer Hall, a 10-bedroom Georgian mansion on the Sandringham estate, where the royal family spends Christmas. Summer holidays are likely to be spend on the Balmoral estate in Scotland.

The Queen is due to be there this weekend, but on Wednesday morning she was able to visit her great-grandson at Kensington Palace, arriving in a green Bentley.

The meeting was historic. It was 120 years since a reigning monarch had met a future king three generations ahead. That last happened in 1894, when Queen Victoria was introduced to the baby who would become Edward VIII.

Three kings are now on hold. The dynasty seems secure, particularly if the leading members go on charming people in this way. The new prince may have to wait a long time for the throne but, God willing, he can expect to be the first king of the 22nd Century. Her Majesty was not thinking about any of that, though, when she told a guest at a reception the night before, “The first born is very special.”

After she left the couple it was revealed that Prince Harry – or Uncle Harry, as he will no doubt love to be known – had stolen into the Kensington Palace unseen, like one of the Apache helicopters he flies. Auntie Pippa and Uncle James Middleton had also been to see the boy. However, the Duke and Duchess did not stay in London for long. By Wednesday afternoon they had left town for the quietness of Bucklebury, where they can get on with learning to be parents, undisturbed.

The Middletons bought a new home last year for £4.85m, and it appears well suited for the task. The Georgian mansion is set in 18 acres, with a swimming pool and tennis court and grounds that are not visible from the outside.

Plenty of members of the constabulary were on hand to make sure of that. Guards stood at both entrances, cars patrolled the country lanes, mounted officers rode their horses around the perimeter and a helicopter hovered overhead with a heat-seeking camera on board, able to spot the best hidden paparazzo.

As they enjoyed the quiet – apart from the chattering blades of the chopper – there was a charming illustration of just how involved people felt with the baby.

Prince Charles was far away, visiting the Royal Welsh Show, when a card was thrust into his hand by 49-year-old Amanda Winney. Inside was a £10 note that she hoped the Duchess of Cambridge would use to buy a cuddly toy for the child.

“He shouldn’t really be here, what with the new baby, but duty calls in his case,” said Mrs Winney. “He took the card and said that he will pass it on, which is fantastic.”

The Prince told one member of the crowd he had been in the dark about the baby’s gender, as the parents had preferred not to know in advance.

The lack of a name at this stage will have been no surprise to him. The Queen took more than a month to tell the world her firstborn was called Charles.

However, just before 6.30pm on Wednesday came the news the bookmakers were waiting for. Yes, it was George. The favourite at 2/1. George Alexander Louis, to be known then as His Royal Highness, Prince George of Cambridge.

There has only been one Prince of Cambridge before, a military man with a racy love life, born in 1819 and commemorated with an equestrian statue in Whitehall.

One day, presumably, the child will be King George VII – although there is an outside chance he will be the eighth, if the Prince of Wales adopts the name in order to avoid the unhappy historical resonances of being a King Charles.

The name George has a distinguished royal history. The first King George took the throne in 1714. Born in Hanover, he barely spoke a word of English. The second was crowned in 1727 and went on to become the last of this nation’s sovereign to fight alongside his own soldiers in battle, against the French.

King George III is best known these days for his madness. He lost the American colonies as well as his sanity, but reigned for nearly 60 years. His son was a prince regent with a notorious love life and lavish habits, although an influential taste in art and ceremony, and he lasted only a decade as king.

There was a pause in the succession of Georges for 80 years before the fifth was crowned in 1910. He saw his country through turbulent times including the First World War and the Great Strike. He also changed the family name from Saxe-Coburg-Gothe to Windsor to appear less German.

His son Albert, known to the family as Bertie, became king after the abdication of Edward VIII in 1936. He didn’t feel up to the job, as portrayed in the film the King’s Speech, but became a much-admired leader during the Second World War. He chose to be George VI in honour of his father.

His death in 1952 led to his daughter, the Princess Elizabeth, becoming Queen. The historian and royal biographer Robert Lacey said: “George is obviously a tribute to the Queen’s father and will, I imagine, give Her Majesty great pleasure.”

The name comes from the Greek for farmer. George the dragon slayer is, of course, the patron saint of England, despite having been born far from here.

George also happens to be one of the middle names of the Prince of Wales, the baby’s grandfather. A poll on the website Mumsnet, long before this baby was born, found that mothers believed boys called George to be “loyal, honest, talented, independent – but with a rebellious streak.” Mumsnet founder Siobhan Freegard said it was “popular, classless and solidly royal”.

The choice of Alexander is a little more of a mystery, although three kings of Scotland have had that name. If it is an attempt to influence the forthcoming Scottish referendum on independence, then it is remarkably subtle. It may instead be inspired by Alexandra, which is one of the Queen’s middle names.

Prince George is unusual among royal children in having only three names. His third is Louis, a reference to Lord Mountbatten, the great uncle and mentor of the Prince of Wales. An admiral, a statesman and the last viceroy of India, he was blown up by the IRA in 1979. That was just three years before the birth of Prince William, who was given Louis as a middle name in tribute. He has now passed it on.

And so the layers of family history, politics and royal duty wrap themselves around the boy who for a short while was just a boy, in a room with his Mum and Dad.

It is likely that he will experience his first royal tour before he is even a year old, as the Cambridges are considering a trip to Australia and New Zealand for early next year. They will not leave him behind, and the loyal citizens of those countries would not forgive them if they did. The less loyal ones might even be won over.

The christening will probably take place before that, in September or October, in the Music Room at Buckingham Palace, with the Archbishop of Canterbury presiding. The baby will wear a robe of Honiton lace lined with satin, a replica of the one used for more than 30 royal christenings. There will surely be a modern twist, too.

Later, Prince George can be expected to go to prep school then boarding school, as both his parents did. Eton is most likely. He will probably attend one of the better universities, then join the armed forces for a while. The combination of camaraderie and privacy helped his father and his Uncle Harry grow up. After that, who knows?

When his father was born there was no internet, no mobile phone network, the Soviet Union and the United States were superpowers and a nuclear apocalypse was the greatest fear. It is all but impossible to predict the way things will be when King George VII takes the throne, at last.

For now, we can at least see that he has been brought into the world by a mother and father who love him, who dote on him, and who will take the greatest care they can of him. The Duke and Duchess of Cambridge seem unusually equipped to teach the boy what he needs to know about the royal life before him, so that it might even become a pleasure.

They are sure to guard his privacy, as best they can, as he grows. And there is no doubt that for his parents, those first four hours alone together in secret with their son will have been among the greatest and most precious moments of their lives.